A Circle Has No End: Role of Cyclic Topology and Accompanying Structural Reorganization on the Hole Distribution in Cyclic and Linear Poly‑p‑phenylene Molecular Wires

π-Conjugated organic oligomers/polymers hold great promise as long-range charge-transfer materials for modern photovoltaic applications. However, a set of criteria for the rational design of functional materials is not yet available, in part because of a lack of understanding of charge distribution in extended π-conjugated systems of different topologies, and concomitant effects on redox and optical properties. Herein we demonstrate the role of cyclic versus linear topology in controlling the redox/optical properties and hole distribution in poly-p-phenylenes (PPs) with the aid of experiment, computation, and our recently developed multistate parabolic model (MPM). It is unequivocally shown that the hole distribution in both cyclic and linear poly-p-phenylene (n ≥ 7) cation radicals is limited to seven p-phenylene units, despite the very different topologies. However, the effect of topology is evidenced in the very different trends in oxidation potentials of cyclic versus linear PPs, which are shown to originate largely from the geometrical distortion of individual p-phenylene units in cyclic PPs. The presence of additional pairwise electronic coupling element in cyclic PPs, absent in linear PPs, plays a significant role only in smaller cyclic PP5 and PP6. This study provides a detailed conceptual description of cyclic and linear poly-p-phenylene cation radicals and demonstrates the versatility and predictive power of MPM, an important new tool for the design and synthesis of novel and efficient charge-transfer materials for molecular electronics and photovoltaic applications, an area of widespread interest

Does Koopmans\u27 Paradigm for 1-Electron Oxidation Always Hold? Breakdown of IP/Eox Relationship for p-Hydroquinone Ethers and the Role of Methoxy Group Rotation

Koopmans’ paradigm states that electron loss occurs from HOMO, thus forming the basis for the observed linear relationships between HOMO/IP, HOMO/Eox, and IP/Eox. In cases where a molecule undergoes dramatic structural reorganization upon 1-electron oxidation, the IP/Eox relationship does not hold, and the origin of which is not understood. For example, X-ray crystallography of the neutral and cation radicals of bicyclo[2.2.1]heptane-annulated p-hydroquinone ethers (THE and MHE) showed that they undergo electron-transfer-induced conformational reorganization and show breakdown of the IP/Eox relationship. DFT calculations revealed that Koopmans’ paradigm still holds true because the electron-transfer-induced subtle conformational reorganization, responsible for the breakdown of IP/Eox relationship, is also responsible for the reordering of HOMO and HOMO-1. Perceived failure of Koopmans’ paradigm in cases of THE and MHE assumes that both vertical and adiabatic electron detachments involve the same HOMO; however, this study demonstrates that the vertical ionization and adiabatic oxidation occur from different molecular orbitals due to reordering of HOMO/HOMO-1. The underpinnings of this finding will spur widespread interest in designing next-generation molecules beyond HQEs, whose electronic structures can be modulated by electron-transfer-induced conformation reorganization

Genetic Algorithm Optimization of Point Charges in Force Field Development: Challenges and Insights

Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields

Two\u27s Company, Three\u27s a Crowd: Exciton Localization in Cofacially Arrayed Polyfluorenes

Understanding the mechanisms of long-range energy transfer through polychromophoric assemblies is critically important in photovoltaics and biochemical systems. Using a set of cofacially arrayed polyfluorenes (Fn), we investigate the mechanism of (singlet) exciton delocalization in π-stacked polychromophoric assemblies. Calculations reveal that effective stabilization of an excimeric state requires an ideal sandwich-like arrangement; yet surprisingly, emission spectroscopy indicates that exciton delocalization is limited to only two fluorene units for all n. Herein, we show that delocalization is determined by the interplay between the energetic gain from delocalization, which quickly saturates beyond two units in larger Fn, and an energetic penalty associated with structural reorganization, which increases linearly with n. With these insights, we propose a hopping mechanism for exciton transfer, based upon the presence of multiple excimeric tautomers of similar energy in larger polyfluorenes (n ≥ 4) together with the anticipated low thermal barrier of their interconversion

Electrostatic Point Charge Fitting as an Inverse Problem: Revealing the Underlying Ill-Conditioning

Atom-centered point charge model of the molecular electrostatics---a major workhorse of the atomistic biomolecular simulations---is usually parameterized by least-squares (LS) fitting of the point charge values to a reference electrostatic potential, a procedure that suffers from numerical instabilities due to the ill-conditioned nature of the LS problem. Here, to reveal the origins of this ill-conditioning, we start with a general treatment of the point charge fitting problem as an inverse problem, and construct an analytically soluble model with the point charges spherically arranged according to Lebedev quadrature naturally suited for the inverse electrostatic problem. This analytical model is contrasted to the atom-centered point-charge model that can be viewed as an irregular quadrature poorly suited for the problem. This analysis shows that the numerical problems of the point charge fitting are due to the decay of the curvatures corresponding to the eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is intrinsic to the problem and related to decreasing electrostatic contribution of the higher multipole moments, that are, in the case of Lebedev grid model, directly associated with the Hessian eigenvectors. For the atom-centered model, this association breaks down beyond the first few eigenvectors related to the high-curvature monopole and dipole terms; this leads to even wider spread-out of the Hessian curvature values. Using these insights, it is possible to alleviate the ill-conditioning of the LS point-charge fitting without introducing external restraints and/or constraints. Also, as the analytical Lebedev grid PC model proposed here can reproduce multipole moments up to a given rank, it may provide a promising alternative to including explicit multipole terms in a force field

Energy Gap between the Poly-\u3cem\u3ep\u3c/em\u3e-phenylene Bridge and Donor Groups Controls the Hole Delocalization in Donor–Bridge–Donor Wires

Poly-p-phenylene wires are critically important as charge-transfer materials in photovoltaics. A comparative analysis of a series of poly-p-phenylene (RPPn) wires, capped with isoalkyl (iAPPn), alkoxy (ROPPn), and dialkylamino (R2NPPn) groups, shows unexpected evolution of oxidation potentials, i.e., decrease (−260 mV) for iAPPn, while increase for ROPPn (+100 mV) and R2NPPn (+350 mV) with increasing number of p-phenylenes. Moreover, redox/optical properties and DFT calculations of R2NPPn/R2NPPn+• further show that the symmetric bell-shaped hole distribution distorts and shifts toward one end of the molecule with only 4 p-phenylenes in R2NPPn+•, while shifting of the hole occurs with 6 and 8 p-phenylenes in ROPPn+• and iAPPn+•, respectively. Availability of accurate experimental data on highly electron-rich dialkylamino-capped R2NPPn together with ROPPn and iAPPn allowed us to demonstrate, using our recently developed Marcus-based multistate model (MSM), that an increase of oxidation potentials in R2NPPn arises due to an interplay between the electronic coupling (Hab) and energy difference between the end-capped groups and bridging phenylenes (Δε). A comparison of the three series of RPPn with varied Δε further demonstrates that decrease/increase/no change in oxidation energies of RPPn can be predicted based on the energy gap Δε and coupling Hab, i.e., decrease if Δε \u3c Hab (i.e., iAPPn), increase if Δε \u3e Hab (i.e., R2NPPn), and minimal change if Δε ≈ Hab (i.e., ROPPn). MSM also reproduces the switching of the nature of electronic transition in higher homologues of R2NPPn+• (n ≥ 4). These findings will aid in the development of improved models for charge-transfer dynamics in donor–bridge–acceptor systems

Does Koopmans’ Paradigm for 1-Electron Oxidation Always Hold? Breakdown of IP/E\u3csub\u3eox\u3c/sub\u3e Relationship for \u3cem\u3ep\u3c/em\u3e-Hydroquinone Ethers and the Role of Methoxy Group Rotation

Koopmans’ paradigm states that electron loss occurs from HOMO, thus forming the basis for the observed linear relationships between HOMO/IP, HOMO/Eox, and IP/Eox. In cases where a molecule undergoes dramatic structural reorganization upon 1-electron oxidation, the IP/Eoxrelationship does not hold, and the origin of which is not understood. For example, X-ray crystallography of the neutral and cation radicals of bicyclo[2.2.1]heptane-annulated p-hydroquinone ethers (THE and MHE) showed that they undergo electron-transfer-induced conformational reorganization and show breakdown of the IP/Eox relationship. DFT calculations revealed that Koopmans’ paradigm still holds true because the electron-transfer-induced subtle conformational reorganization, responsible for the breakdown of IP/Eox relationship, is also responsible for the reordering of HOMO and HOMO-1. Perceived failure of Koopmans’ paradigm in cases of THE and MHE assumes that both vertical and adiabatic electron detachments involve the same HOMO; however, this study demonstrates that the vertical ionization and adiabatic oxidation occur from different molecular orbitals due to reordering of HOMO/HOMO-1. The underpinnings of this finding will spur widespread interest in designing next-generation molecules beyond HQEs, whose electronic structures can be modulated by electron-transfer-induced conformation reorganization

A Search for Blues Brothers: X-ray Crystallographic/Spectroscopic Characterization of the Tetraarylbenzidine Cation Radical as a Product of Aging of Solid Magic Blue

Magic blue (MB+˙ SbCl6− salt), i.e. tris-4-bromophenylamminium cation radical, is a routinely employed one-electron oxidant that slowly decomposes in the solid state upon storage to form so called ‘blues brothers’, which often complicate the quantitative analyses of the oxidation processes. Herein, we disclose the identity of the main ‘blues brother’ as the cation radical and dication of tetrakis-(4-bromophenyl)benzidine (TAB) by a combined DFT and experimental approach, including isolation of TAB+˙ SbCl6− and its X-ray crystallography characterization. The formation of TAB in aged magic blue samples occurs by a Scholl-type coupling of a pair of MB followed by a loss of molecular bromine. The recognition of this fact led us to the rational design and synthesis of tris(2-bromo-4-tert-butylphenyl)amine, referred to as ‘blues cousin’ (BC: Eox1 = 0.78 V vs. Fc/Fc+, λmax(BC+˙) = 805 nm, εmax = 9930 cm−1 M−1), whose oxidative dimerization is significantly hampered by positioning the sterically demanding tert-butyl groups at the para-positions of the aryl rings. A ready two-step synthesis of BC from triphenylamine and the high stability of its cation radical (BC+˙) promise that BC will serve as a ready replacement for MB and an oxidant of choice for mechanistic investigations of one-electron transfer processes in organic, inorganic, and organometallic transformations

From Wires to Cables: Attempted Synthesis of 1,3,5-Trifluorenylcyclohexane as a Platform for Molecular Cables

Multiple molecular wires braided together in a single assembly, termed as molecular cable, are promising next-generation materials for effective long-range charge transport. As an example of the platform for constructing molecular cables, 1,3,5-trifluorenylcyclohexane (TFC) and its difluorenyl analogues (DFCs) were systematically investigated both experimentally (X-ray crystallography) and theoretically (DFT calculations). Although the syntheses of DFCs were successfully achieved, the synthesis of TFC, which involved a similar intramolecular Friedel–Crafts cyclization as the last step, was unsuccessful. An exhaustive study of the conformational landscape of cyclohexane ring of TFC and DFCs revealed that TFC is a moderately strained molecule (∼17 kcal/mol), and computational studies of the reaction profile show that this steric strain, present in the transition state, is responsible for the unusually high (∼5 years) reaction half-life. A successful synthesis of TFC will require that the steric strain is introduced in multiple steps, and such alternative strategies are being currently explored